Fermiology, charge transfer energy, and robust paramagnons in high-$T_c$ cuprate superconductors

Abstract: Copper-oxide high-temperature (high-$T_c$) superconductors host robust paramagnon excitations whose propagation energies are insensitive to hole concentration and correlate with maximal measured superconducting transition temperatures. Given variation of electronic structure across (and within) cuprate families, elucidation of the relationship between microscopic parameters relevant to high-$T_c$ superconductivity and paramagnon dynamics remains a key challenge to theory. Employing canonical Hubbard- and $t$-$J$-$U$ models of a $\mathrm{CuO_2}$ plane, we relate robust paramagnon energies to high-$T_c$ fermiology (via the ratio $r \equiv t<sup>\prime/|t|$ of next-nearest- to nearest-neighbor hopping integrals) and charge transfer energy, $Δ<em>\mathrm{CT}$. It is shown that variation of $r$ and $Δ</em>\mathrm{CT}$ between materials has an opposite effect on paramagnon energy, rationalizing comparable bandwidth of magnetic excitations across multiple cuprates. Utilizing empirical values of $r$ and $Δ_\mathrm{CT}$ as input to theory, we address magnetic dynamics in Bi-family of cuprates with up to three $\mathrm{CuO_2}$ planes, and demonstrate quantitative (within $6\,\%$ margin) agreement of calculated paramagnon energies with experiment. Our work offers a route toward quantitative control of robust paramagnon physics in strongly-correlated electron systems.